Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
450.1-a4
450.1-a
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
450.1
\( 2 \cdot 3^{2} \cdot 5^{2} \)
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \)
$1.16409$
$(a), (3), (5)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$1$
$2.808889283$
0.662061553
\( \frac{35578826569}{5314410} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
3600.1-g4
3600.1-g
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3600.1
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{14} \cdot 3^{24} \cdot 5^{2} \)
$1.95776$
$(a), (3), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{4} \cdot 3 \)
$1$
$2.683744567$
2.846540973
\( \frac{35578826569}{5314410} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -274\) , \( 1550\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-274{x}+1550$
4050.1-a4
4050.1-a
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4050.1
\( 2 \cdot 3^{4} \cdot 5^{2} \)
\( 2^{2} \cdot 3^{36} \cdot 5^{2} \)
$2.01626$
$(a), (3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$1$
$1.789163044$
1.265129321
\( \frac{35578826569}{5314410} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -617\) , \( 5231\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-617{x}+5231$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.